Aumann, T.

Chulkov, L. V.

Jonson, B.

Marganiec, J.

Nilsson, T.

Simon, H.

Wamers, F.

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Thomas-Ehrman shiftsT. Aumann1,2, L.V. Chulkov1,3, B. Jonson4, J. Marganiec1,2, T. Nilsson4, H. Simon1, F. Wamers1,2, andthe R3B Collaboration1Technische Universita¨t, Darmstadt; 2GSI, Darmstadt; 3NRC Kurchatov Institute, Moscow; 4Chalmers TekniskaHo¨gskola, Go¨teborgThe Thomas-Ehrman shift (TES) is a very importantcharacteristic of the mirror asymmetries related to thestructure of nuclei with weakly-bound protons. The TES isespecially large when the participating states are unboundagainst proton emission and when the occupation of thes-shell is large. This is demonstrated in Table 1, whereTES for neon isotopes with core+2p structure and their re-spective mirror nuclei are given. TES is defined as the dif-ference between the excitation energy differences betweenmirror states with spins I1 and I2:TES(I1, I2) = [E(I1)−E(I2)]p− [E(I1)−E(I2)]n. (1)Table 1: Thomas-Ehrman shifts for neon isotopes withcore+2p structure and their mirror nuclei. S2p is the two-proton separation energy and P (s2) the amount of s2 in thewave function [1, 2]. Uncertainties smaller than 1 keV arenot indicated.Isotope S2p (MeV) P (s2) Mirror TES (MeV)18Ne 4.523 19% 18O -0.0952+; 0+17Ne 0.973(27) 24% 17N -0.086(8)3/2−; 1/2−16Ne -1.388(15) 46% 16C 0.070(46)2+; 0+15Ne -2.552(66) 63% 15B 0.573(78)5/2−; 3/2−Attempts to describe the TES for the nuclei 17Ne and16Ne were made in Refs. [3, 4] within a three-body model,with inert core plus two protons. The conclusion given inRef. [3] was: “The computed three-body Thomas-Ehrmanshifts are then meaningful although relatively inaccurate”.The progress in the spectroscopy of exotic nuclei hasgiven access to isospin multiplets in their ground and ex-cited states. Investigation of isospin symmetry in theisobaric analog states and the properties of the IsobaricMultiplet Mass Equation (IMME) was recently made inRefs. [5, 6]. We have made an IMME analysis using theknown masses and excited states of the A = 16 quintet.Table 2 gives the result of a least-square fit to the masses ofthe 0+ and 2+ states for T = 2 isobaric A = 16 multiplet.Usually the Thomas-Ehrman shift is given as the differ-ence in energies of excited states in mirror nuclei. Here wepropose a broader understanding of the TES by analysingTable 2: Coefficients in the Isobaric Multiplet Mass Equa-tion obtained from a fit to experimental data.State a (keV) b (keV) c (keV) χ2min/10+ 17982(3) -2572(4) 213(2) 3.292+ 19771(8) -2598(10) 220(4) 3.68the dependence of the positions of excited states on theisospin projection. With the IMME coefficients we maycalculate TES for members of the T = 2, A = 16 multipletand deduce the energies of the unknown excited 0+ and 2+states in 16F (Fig. 1). We thus predict the 0+ state at E∗ =10.087(10) MeV and the 2+ state at E∗ = 11.908(14)MeV, which is in good agreement with the estimate madeby Fortune [7].1201008060402000-2 -1 1 2TzTES (keV)A=16, T=2NeFONCFigure 1: Thomas-Ehrman shift between 2+ and 0+ statesfor members of the isobaric quintet (A = 16, T = 2) as afunction of the isospin projection.References[1] H.T. Fortune, Phys. Lett. B 718, 1342 (2013).[2] F. Wamers et al., Phys. Rev. Lett. 112, 132502 (2014).[3] E. Garrido et al., Phys. Rev. C 69, 024002 (2004).[4] L.V. Grigorenko et al., arXiv:1411.1846[nucl-th], 2014.[5] M. MacCormik, G. Audi, Nucl. Phys. A 925, 61 (2014); Er-ratum Nucl. Phys. A 925, 296 (2014).[6] Y.H. Lam et al., At. Nucl. Data Tables 99, 680 (2013).[7] H.T. Fortune, Phys. Rev. C 74, 054310 (2006).GSI SCIENTIFIC REPORT 2014 MU-NUSTAR-NR-03DOI:10.15120/GR-2015-1-MU-NUSTAR-NR-03 187

Thomas-Ehrman shifts

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Thomas-Ehrman shifts

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